# How do you solve x^2 + 6x + 9 = 0 by factoring?

Oct 8, 2015

color(blue)(x=-3

#### Explanation:

${x}^{2} + 6 x + 9 = 0$

We can Split the Middle Term of this expression to factorise it and thereby find the solution.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 9 = 9$

AND

${N}_{1} + {N}_{2} = b = 6$

After trying out a few numbers we get ${N}_{1} = 3$ and ${N}_{2} = 3$
$3 \cdot 3 = 9$, and $3 + 3 = 6$

${x}^{2} + \textcolor{b l u e}{6 x} + 9 = {x}^{2} + \textcolor{b l u e}{3 x + 3 x} + 9$

$x \left(x + 3\right) + 3 \left(x + 3\right) = 0$

$\left(x + 3\right) \left(x + 3\right) = 0$

We now equate the factor to zero to obtain the solution (both factors are equal here).
$x + 3 = 0$
color(blue)(x=-3 is the solution.